A First-Principles Implementation of Scale Invariance Using Best Matching

          @misc{ pirsa_PIRSA:09090100,
            doi = {10.48660/09090100},
            url = {https://pirsa.org/09090100},
            author = {Westman, Hans},
            keywords = {Quantum Foundations},
            language = {en},
            title = {A First-Principles Implementation of Scale Invariance Using Best Matching},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {sep},
            note = {PIRSA:09090100 see, \url{https://pirsa.org}}
          }
          

Abstract

We present a first-principles implementation of {\em spatial} scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching. In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential A_k as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious, but physically questionable, theory, the equations of motion of this new theory are second order in time-derivatives. It is tempting to try to interpret the vector potential A_k as the electromagnetic field. We exhibit four independent reasons for not giving into this temptation. A more likely possibility is that it can play the role of ``dark matter''. Indeed, as noted in scale invariance seems to play a role in the MOND phenomenology. Spatial boundary conditions are derived from the free-endpoint variation method and a preliminary analysis of the constraints and their propagation in the Hamiltonian formulation is presented.